Multi-fluid stratified shear flows in pipes. Part 2. Critical conditions in the development of interfacial profiles

Abstract:

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.

The focus of this paper is on mathematical formulation and
computation of critical flow conditions in horizontal or nearly
horizontal pipes. Continuity and momentum equations are
derived considering an arbitrary number of fluids and then
rearranged so as to yield a system of ordinary differential
equations. It is shown that the matrix of the system needs to be
invertible so as to compute interfacial profiles. Critical
conditions are recognised as those for which the matrix
becomes singular and the hypothesis of gradually varied flow
fails. Some well known results of linear algebra are here used
to define criteria capable of discerning between geometric and
kinematic conditions of the flow which are certainly noncritical
and others which may or may not be critical.